We study force-free magnetospheres in the Blandford-Znajek process from rapidly rotating black holes by adopting the near-horizon geometry of near-extreme Kerr black holes (near-NHEK). It is shown that the Znajek regularity condition on the horizon c
an be directly derived from the resulting stream equation. In terms of the condition, we split the full stream equation into two separate equations. Approximate solutions around the rotation axis are derived. They are found to be consistent with previous solutions obtained in the asymptotic region. The solutions indicate energy and angular-momentum extraction from the hole.
Based upon projected local density of states (PLDOS) for photons, we develop a local coupling theory to simultaneously treat the weak and strong interaction between a quantum emitter and photons in arbitrary nanostructures. The PLDOS is mapped by an
extremely flexible and efficient method. The recent experiment observation for the photonic crystal slabs is very well interpreted by our ab-initio PLDOS. More importantly, a bridge linking the PLDOS and cavity quantum electrodynamics is for the first time established to settle quality factor, g factor and vacuum Rabi splitting. Our work greatly enriches the knowledge about the interaction between light and matter in nanostructures.
Knowledge bases of entities and relations (either constructed manually or automatically) are behind many real world search engines, including those at Yahoo!, Microsoft, and Google. Those knowledge bases can be viewed as graphs with nodes representin
g entities and edges representing (primary) relationships, and various studies have been conducted on how to leverage them to answer entity seeking queries. Meanwhile, in a complementary direction, analyses over the query logs have enabled researchers to identify entity pairs that are statistically correlated. Such entity relationships are then presented to search users through the related searches feature in modern search engines. However, entity relationships thus discovered can often be puzzling to the users because why the entities are connected is often indescribable. In this paper, we propose a novel problem called entity relationship explanation, which seeks to explain why a pair of entities are connected, and solve this challenging problem by integrating the above two complementary approaches, i.e., we leverage the knowledge base to explain the connections discovered between entity pairs. More specifically, we present REX, a system that takes a pair of entities in a given knowledge base as input and efficiently identifies a ranked list of relationship explanations. We formally define relationship explanations and analyze their desirable properties. Furthermore, we design and implement algorithms to efficiently enumerate and rank all relationship explanations based on multiple measures of interestingness. We perform extensive experiments over real web-scale data gathered from DBpedia and a commercial search engine, demonstrating the efficiency and scalability of REX. We also perform user studies to corroborate the effectiveness of explanations generated by REX.
